Nikfard Tayebe, Tabatabaei Yahya Hematyar, Shahbazi Farhad
Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran.
Phys Rev E. 2021 Nov;104(5-1):054213. doi: 10.1103/PhysRevE.104.054213.
We numerically study Kuramoto model synchronization consisting of the two groups of conformist-contrarian and excitatory-inhibitory phase oscillators with equal intrinsic frequency. We consider random and small-world (SW) topologies for the connectivity network of the oscillators. In random networks, regardless of the contrarian to conformist connection strength ratio, we found a crossover from the π-state to the blurred π-state and then a continuous transition to the incoherent state by increasing the fraction of contrarians. However, for the excitatory-inhibitory model in a random network, we found that for all the values of the fraction of inhibitors, the two groups remain in phase and the transition point of fully synchronized to an incoherent state reduced by strengthening the ratio of inhibitory to excitatory links. In the SW networks we found that the order parameters for both models do not show monotonic behavior in terms of the fraction of contrarians and inhibitors. Up to the optimal fraction of contrarians and inhibitors, the synchronization rises by introducing the number of contrarians and inhibitors and then falls. We discuss that the nonmonotonic behavior in synchronization is due to the weakening of the defects already formed in the pure conformist and excitatory agent model in SW networks. We found that in SW networks, the optimal fraction of contrarians and inhibitors remain unchanged for the rewiring probabilities up to ∼0.15, above which synchronization falls monotonically, like the random network. We also showed that in the conformist-contrarian model, the optimal fraction of contrarians is independent of the strength of contrarian links. However, in the excitatory-inhibitory model, the optimal fraction of inhibitors is approximately proportional to the inverse of inhibition strength.
我们对由两组具有相同固有频率的顺应者 - 叛逆者和兴奋性 - 抑制性相位振荡器组成的Kuramoto模型同步进行了数值研究。我们考虑了振荡器连接网络的随机和小世界（SW）拓扑结构。在随机网络中，无论叛逆者与顺应者的连接强度比如何，我们发现通过增加叛逆者的比例，会出现从π态到模糊π态的转变，然后是向非相干态的连续转变。然而，对于随机网络中的兴奋性 - 抑制性模型，我们发现对于抑制剂比例的所有值，两组都保持同相，并且通过增强抑制与兴奋连接的比例，完全同步到非相干态的转变点降低。在SW网络中，我们发现两个模型的序参量在叛逆者和抑制剂比例方面都不表现出单调行为。直到叛逆者和抑制剂的最佳比例，同步通过引入叛逆者和抑制剂的数量而增加，然后下降。我们讨论了同步中的非单调行为是由于SW网络中纯顺应者和兴奋性代理模型中已经形成的缺陷的减弱。我们发现，在SW网络中，对于高达约0.15的重新布线概率，叛逆者和抑制剂的最佳比例保持不变，高于此值时同步像随机网络一样单调下降。我们还表明，在顺应者 - 叛逆者模型中，叛逆者的最佳比例与叛逆者链接的强度无关。然而，在兴奋性 - 抑制性模型中，抑制剂的最佳比例近似与抑制强度的倒数成正比。
